Home
Class 12
MATHS
If sin theta = cos theta ,then the valu...

If ` sin theta = cos theta` ,then the value of `2 tan^(2) theta + sin^(2) theta -1` is equal to

A

`1/2`

B

`5/2`

C

`3/2`

D

2

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we start with the given equation: **Step 1: Understand the equation** Given that \( \sin \theta = \cos \theta \). **Step 2: Find the relationship between sine and cosine** From the equation \( \sin \theta = \cos \theta \), we can divide both sides by \( \cos \theta \) (assuming \( \cos \theta \neq 0 \)): \[ \frac{\sin \theta}{\cos \theta} = 1 \] This simplifies to: \[ \tan \theta = 1 \] **Step 3: Determine the angle** The angle \( \theta \) for which \( \tan \theta = 1 \) is: \[ \theta = 45^\circ \quad \text{(or } \frac{\pi}{4} \text{ radians)} \] **Step 4: Calculate \( \tan^2 \theta \) and \( \sin^2 \theta \)** Now, we can find \( \tan^2 \theta \) and \( \sin^2 \theta \): \[ \tan^2 45^\circ = 1^2 = 1 \] \[ \sin 45^\circ = \frac{1}{\sqrt{2}} \quad \Rightarrow \quad \sin^2 45^\circ = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2} \] **Step 5: Substitute into the expression** Now we substitute these values into the expression \( 2 \tan^2 \theta + \sin^2 \theta - 1 \): \[ 2 \tan^2 \theta + \sin^2 \theta - 1 = 2(1) + \frac{1}{2} - 1 \] **Step 6: Simplify the expression** Calculating this step-by-step: \[ = 2 + \frac{1}{2} - 1 \] \[ = 2 - 1 + \frac{1}{2} \] \[ = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \] **Final Answer:** Thus, the value of \( 2 \tan^2 \theta + \sin^2 \theta - 1 \) is: \[ \frac{3}{2} \] ---

To solve the problem, we start with the given equation: **Step 1: Understand the equation** Given that \( \sin \theta = \cos \theta \). **Step 2: Find the relationship between sine and cosine** From the equation \( \sin \theta = \cos \theta \), we can divide both sides by \( \cos \theta \) (assuming \( \cos \theta \neq 0 \)): \[ ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 Trigonomertric Ratio of Allied Angle|18 Videos
  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos
  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|20 Videos

Similar Questions

Explore conceptually related problems

If sin theta+cos theta=1, then the value of sin2 theta is equal to

Ifcos 2 theta+9sin2 theta+6sin theta+54cos theta=1 then the value of 100tan^(2)theta+9tan theta is equal to

Knowledge Check

  • If (sin theta + cos theta)/(sin theta - cos theta) = (5)/(4) , the value of (tan^(2) theta + 1)/(tan^(2) theta - 1) is

    A
    `(25)/(16)`
    B
    `(41)/(9)`
    C
    `(41)/(40)`
    D
    `(40)/(41)`
  • If (3sin 2 theta)/(5+4cos2theta)=1 , then the value of tan theta is equal to

    A
    1
    B
    `1//3`
    C
    3
    D
    none of these
  • If sin theta=cos theta , then 2tan^(2)theta+sin^(2)theta-1= _____

    A
    `(-3)/2`
    B
    `3/2`
    C
    `2/3`
    D
    `(-2)/3`
  • Similar Questions

    Explore conceptually related problems

    If theta is an acute angle and sin theta=cos theta, find the value of 2tan^(2)theta+sin^(2)theta-1

    If cos theta + sin theta =sqrt2 cos theta , then the value of (cos theta -sin theta)/(sin theta) is

    If sin theta=cos theta then 2tan theta+cos^(2)theta=

    If 3 sin theta=4 cos theta , then tan^2 theta+sin theta-cos theta is equal to : यदि 3 sin theta=4 cos theta , है, तो tan^2 theta+sin theta-cos theta का मान किसके बराबर है?

    If 29 tan theta = 31 then the value of (1 +2 sin theta cos theta)/(1- 2 sin theta cos theta) is equal to